THE GENERALIZED GRADED UNFOLDING MODEL: A GENERAL PARAMETRIC ITEM RESPONSE MODEL FOR UNFOLDING GRADED RESPONSES

Abstract

Psychologists have long used binary or graded disagree-agree responses to measure attitudes. Such data have traditionally been analyzed with cumulative models, but several researchers have recently argued that unfolding models are generally more appropriate. There have been several parametric item response models proposed to unfold disagree-agree responses. Some of these models allow only for binary responses whereas others permit both binary and graded responses. A new item response model, referred to as the Generalized Graded Unfolding Model (GGUM), is developed in this paper. The GGUM allows for either binary or graded responses and generalizes previous item response models for unfolding in two useful ways. First, it implements a discrimination parameter that varies across items, and thus, items are allowed to discriminate among respondents in different ways. Second, the GGUM allows for distinctively different use of response categories across items. It does this by implementing response category threshold parameters that vary across items. A marginal maximum likelihood algorithm is implemented to estimate GGUM item parameters, whereas person parameters are derived from an expected a posteriori technique. Recovery simulations suggest that accurate item parameter estimates can be obtained with approximately 750 subjects. Additionally, accurate person estimates are derived with approximately 20 6-category items. The applicability of the GGUM to common attitude testing situations is illustrated with real data on student attitudes toward abortion. Index terms: attitude measurement, unfolding model, item response theory, graded unfolding model, generalized graded unfolding model, Thurstone scale, Likert scale.